In small-size samples, the translational and inversion symmetry is naturally broken at the edges, which gives rise to additional (edge-related) sources
of second-order nonlinearity. The corresponding photogalvanic currents flowing along the edges and controlled by the electromagnetic field polarization have been observed in single and bilayer graphene [1]}, [2]}, [3]}, [4]}.
A kinetic theory of the edge photogalvanic effects has been developed for the intraband (Drude-like) optical transitions [1]}, [2]}, [7]}, inter-Landau level transitions [3]}, interband one-photon [9]} and two-photon absorption [4]} in
2D Dirac materials. Edge effects in SHG response have been observed in 2D layers of transition metal dichalcogenides in the spectral range of interband transitions and attributed to the local modification of atomic and electronic structures at the edges [11]}, [12]}. The edge SHG induced by non-linear transport of 2D electron gas at the edge remains unexplored so far.
